Carbon Footprint-Driven Multi-Objective Scheduling Optimization for Flexible Job Shops

This study proposes a tri-objective optimization model for low-carbon scheduling in flexible job shop environments, aiming to minimize makespan, carbon emissions and operational costs while incorporating handling and adjustment constraints. To solve the proposed model, an improved non-dominated sorting dung beetle optimizer (INDBO) is developed, integrating GLR-based initialization, a hybrid IPOX–UX crossover operator and non-dominated sorting with crowding distance estimation. Experimental evaluation based on a realistic case involving multiple jobs and machines demonstrates that INDBO achieves superior Pareto solution quality—evidenced by higher hypervolume values—and more favorable trade-offs between carbon emissions and cost while maintaining competitive makespan performance compared to baseline algorithms. The results indicate that the proposed approach not only exhibits enhanced performance in the conducted experiments but also holds practical potential for advancing energy-efficient and sustainable manufacturing practices.